Bias and Sampling Error of the Estimated Proportion of Genotypic Variance Explained by Quantitative Trait Loci Determined From Experimental Data in Maize Using Cross Validation and Validation With Independent Samples

Abstract

Cross validation (CV) was used to analyze the effects of different environments and different genotypic samples on estimates of the proportion of genotypic variance explained by QTL (p). Testcrosses of 344 F(3) maize lines grown in four environments were evaluated for a number of agronomic traits. In each of 200 replicated CV runs, this data set was subdivided into an estimation set (ES) and various test sets (TS). ES were used to map QTL and estimate p for each run (p(ES)) and its median (p(ES)) across all runs. The bias of these estimates was assessed by comparison with the median (p(TS.ES)) obtained from TS. We also used two independent validation samples derived from the same cross for further comparison. The median p(ES) showed a large upward bias compared to p(TS.ES). Environmental sampling generally had a smaller effect on the bias of p(ES) than genotypic sampling or both factors simultaneously. In independent validation, p(TS.ES) was on average only 50% of p(ES). A wide range among p(ES) reflected a large sampling error of these estimates. QTL frequency distributions and comparison of estimated QTL effects indicated a low precision of QTL localization and an upward bias in the absolute values of estimated QTL effects from ES. CV with data from three QTL studies reported in the literature yielded similar results as those obtained with maize testcrosses. We therefore recommend CV for obtaining asymptotically unbiased estimates of p and consequently a realistic assessment of the prospects of MAS.